Detailed computer experiments have been performed to investigate the behaviors of propagating solitary-waves in a new nonlinear transmission line determined by the following equations: \frac{\partial}{\partial{t}} 0 ln (1+in/i0)=υn-1(t)-υn(t) \frac{\partial}{\partial{t}} Q0 ln (1+υn/υ0)=in(t)-in+1(t) These nonlinearities originate from Volterra's nonlinear competition equations. Solitary-waves which propagate along the line exhibiting a soliton-like nature are found. Interesting behaviors of interactions between solitary-waves have been revealed by a computer simulation. Compasisons with nonlinear transmission lines previously treated are presented.